Question

. A woman is twice the age of her daughter today. Ten
years ago, the woman was thrice as old as her
daughter. What was the age of the woman at the
time of her daughter's birth?
A) 16
B) 18
C) 20
D) 24​

Answer 1

Answer:

The age of woman at the time of her daughter's birth = 20 years

Step-by-step explanation:

Let the age of her daughter be x years.

Given that:

• A woman is twice the age of her daughter today.

→ Woman's age = 2x years.

Ten years ago,

• The woman was thrice as old as her daughter.

→ (2x - 10) = 3(x - 10)

→ 2x - 10 = 3x - 30

→ 3x - 2x = 30 - 10

→ x = 20

• Age of daughter = x = 20 years
• Age of woman = 2x = 2 × 20 = 20 years

Finding the age of woman at the time of her daughter's birth:

= Present age of woman - Present age of daughter

= 40 years - 20 years

= 20 years

Answer 2

$\Large \underline{ \frak{ \: \: \: \: \: \: \: \: \: \: \: \bigstar \pink{ Required \: solution }\: \: \: \: \: \: \: \: \: \: \: }}$

Given:

• A women is twice the age of her daughter today

• Ten years ago the women was thrice as old as her daughter

To find:

• age of women at the time of her daughter's age

Solution:

Let present age of daughter be x

.°. mother's present age will be 2x

Ten years ago:

• Daughter age = x - 10
• Mother's age = 2x -10

$\bigstar \underline{\boldsymbol{According \: to \: question: }}$

Ten years ago:

$\dashrightarrow \sf{}Mothe'rs \: age = 3 \times daughter's \: age$

$\dashrightarrow \sf{}3(x - 10) = 2x - 10$

$\dashrightarrow \sf{}3(x) - 3(10) = 2x - 10$

$\dashrightarrow \sf{}3x - 30 = 2x - 10$

$\dashrightarrow \sf{}3x - 2x - 30 = - 10$

$\dashrightarrow \sf{}x - 30 = - 10$

$\dashrightarrow \sf{}x= - 10 + 30$

$\dashrightarrow \underline {\boxed {\sf{}x= 20}}$

Verification:

• 3(x - 10) = 2x - 10

put value of x in this equation

• 3(20 - 10) = 2 × 20 -10

• 3(20)-3(10) = 40 - 10

• 60 - 30 = 30

• 30 = 30

LHS = RHS

hence verified!

Finally:

Age of the woman at the time of her daughter's birth:

• Present age of women- Present age of daughter

• 2x - x

• 2 × 20 - 20

• 40 - 20

• 20 years

$\therefore \underline{ \text{Age of the woman at the time of her daughter's birth \: = 20 years}}$